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What will be the base impedance for a three-phase system with base MVA = 100 MVA and base kV as 11 kV?
1. 1.21 Ohms
2. 3.6 Ohms
3. 5.2 Ohms
4. 2.78 Ohms

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Correct Answer - Option 1 : 1.21 Ohms

Concept:

Base impedance is given by

\({Z_{base}} = \frac{{kV_{base}^2}}{{MV{A_{base}}}}\)

kVbase is base voltage rating

MVAbase is base MVA rating

Calculation:

Given that, base kV = 11 kV

Base MVA = 100 MVA

Base impedance, \({Z_{base}} = \frac{{{{11}^2}}}{{100}} = 1.21\;{\rm{\Omega }}\)

Important:

The relation between new per-unit value & old per unit value impedance

\({({Z_{pu}})_{new}}\; = {({Z_{pu}})_{old}} \times {\left( {\frac{{k{V_{base}}}}{{k{V_{new}}}}} \right)^2} \times \;\left( {\frac{{MV{A_{new}}}}{{MV{A_{old}}}}} \right)\)

Also \({Z_{pu}} = \frac{{{Z_{Actual}}}}{{{Z_{base}}}}\)

 \({Z_{base}} = \frac{{kV_{base}^2}}{{MV{A_{base}}}}\)

Where,

(Zpu)new = New per unit value of impedance

(Zpu)old = Old per unit value of impedance

kVbase = Old base value of voltage

kVnew = New base value of voltage

MVAnew = New base value of power

MVAold = Old base value of power

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